A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass m 2 collides with A with a velocity which is half v → 2 the instantaneous velocity v → of A. The collision is completely inelastic. Then, the combined body:

starts moving in an elliptical orbit around the planet

continues to move in a circular orbit

Escapes from the Planet's Gravitational field

Falls vertically downwards towards the planet

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A hollow circular tube of radius $R$ and negligible internal diameter is fixed on horizontal surface. Ball $A$ of mass $m$ is given velocity $v_{\circ}$ in the shown direction. It collides with ball $B$ of mass $2 m$ . Collision is perfectly elastic. If centre of loop is origin of co-ordinate system, then co-ordinate of next collision is

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Important Questions on Work, Energy and Power

MEDIUM

Physics>Mechanics>Work, Energy and Power>Collisions

A body A of mass

m

is moving in a circular orbit of radius

R

about a planet. Another body B of mass

\frac{m}{2}

collides with A with a velocity which is half

(\frac{\vec{v}}{2})

the instantaneous velocity

\vec{v}

of A. The collision is completely inelastic. Then, the combined body:

HARD

Physics>Mechanics>Work, Energy and Power>Collisions

A small particle of mass

m

moving inside a heavy, hollow and straight tube along the tube axis, undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is

L = L_{0}

the particle speed is

v = v_{0} .

The piston is moved inward at a very low speed

V

such that

V ≪ \frac{d L}{L} v_{0},

where

d L

is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?

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HARD

Physics>Mechanics>Work, Energy and Power>Collisions

A particle of mass

m

is dropped from a height

h

above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of

\sqrt{2 g h} .

If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of

\sqrt{\frac{h}{g}}

is:

EASY

Physics>Mechanics>Work, Energy and Power>Collisions

Two identical balls

A

and

B

having velocities of

0.5 m s^{- 1}

and

- 0.3 m s^{- 1}

, respectively, collide elastically in one dimension. The velocities of

B

and

A

after the collision, respectively, will be

HARD

Physics>Mechanics>Work, Energy and Power>Collisions

A simple pendulum, made of a string of length

l

and

a

bob of mass

m,

is released from a small angle

θ_{0} .

It strikes a block of mass

M,

kept on horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle

θ_{1} .

Then

M

is given by:

HARD

Physics>Mechanics>Work, Energy and Power>Collisions

A particle of mass m is projected with a speed u from the ground at an angle

θ = \frac{π}{3}

w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity

u \hat{i} .

The horizontal distance covered by the combined mass before reaching the ground is:

EASY

Physics>Mechanics>Work, Energy and Power>Collisions

A block of mass

m

moving on a frictionless surface at speed

v

collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle

θ

with its initial direction and has speed

v_{1}

. The speed of the second block after the collision is

MEDIUM

Physics>Mechanics>Work, Energy and Power>Collisions

Particle

A

of mass

m_{1}

moving with velocity

(\sqrt{3} \hat{i} + \hat{j}) {ms}^{- 1}

collides with another particle

B

of mass

m_{2}

which is at rest initially. Let

{\vec{v}}_{1}

and

{\vec{v}}_{2}

be the velocities of particles

A

and

B

after collision respectively. If

m_{1} = 2 m_{2}

and after collision

{\vec{v}}_{1} - (\hat{i} + \sqrt{3} \hat{j}) {ms}^{- 1}

, the angle between

{\vec{v}}_{1}

and

{\vec{v}}_{2}

is :

EASY

Physics>Mechanics>Work, Energy and Power>Collisions

On a frictionless surfaces, a block of mass

M

moving at speed

v

collides elastically with another block of same mass

M

which is initially at rest. After collision the first block moves at an angle

θ

to its initial direction and has a speed

\frac{v}{3}

. The second block's speed after the collision is:

HARD

Physics>Mechanics>Work, Energy and Power>Collisions

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy

K

with

t

time most appropriately? The figures are only illustrative and not to the scale.

MEDIUM

Physics>Mechanics>Work, Energy and Power>Collisions

A satellite of mass

M

is in a circular orbit of radius

R

about the center of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastic. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:

HARD

Physics>Mechanics>Work, Energy and Power>Collisions

Two particles

A

and

B

of equal mass

M

are moving with the same speed

v

as shown in figure. They collide completely inelastic and move as a single particle

C

. The angle

θ

that the path of

C

makes with the

X

-axis is given by-

Question Image

EASY

Physics>Mechanics>Work, Energy and Power>Collisions

During inelastic collision between two objects, which of the following quantity always remains conserved?

MEDIUM

Physics>Mechanics>Work, Energy and Power>Collisions

Two particles of equal mass

m

have respective initial velocities

u \hat{i}

and

u (\frac{\hat{i} + \hat{j}}{2})

. They collide completely inelastically. The energy lost in the process is:

MEDIUM

Physics>Mechanics>Work, Energy and Power>Collisions

A block of mass

1.9 kg

is at rest at the edge of a table, of height 1 m. A bullet of mass

0.1 kg

collides with the block and sticks to it. If the velocity of the bullet is

20 m s^{- 1}

in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take

g = 10 m s^{- 2}

. Assume there is no rotational motion and loss of energy after the collision is negligible.]

MEDIUM

Physics>Mechanics>Work, Energy and Power>Collisions

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial velocities of the two bodies (in degree) is -

EASY

Physics>Mechanics>Work, Energy and Power>Collisions

Blocks of masses

m, 2 m, 4 m

and

8 m

are arranged in a line of a frictionless floor. Another block of mass

m

, moving with speed

υ

along the same line (see figure) collides with mass

m

in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass

8 m

starts moving the total energy loss is

p %

of the original energy. Value of

p

is close to:
Question Image

HARD

Physics>Mechanics>Work, Energy and Power>Collisions

A body

A

of mass

m = 0.1 k g

has an initial velocity of

3 \hat{i} m s^{- 1}

. It collides elastically with another body

B

of the same mass which has an initial velocity of

5 \hat{j} m s^{- 1}

. After the collision,

A

moves with a velocity

\vec{v} = 4 (\hat{i} + \hat{j}) m s^{- 1}

. The energy of

B

after the collision is written as

\frac{x}{10} J

. The value of

x

HARD

Physics>Mechanics>Work, Energy and Power>Collisions

In a collinear collision, a particle with an initial speed

v_{0}

strikes a stationary particle of the same mass. If the final total kinetic energy is

50 %

greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after the collision, is

MEDIUM

Physics>Mechanics>Work, Energy and Power>Collisions

A particle of mass

m

moving in the

x

direction with speed

2 v

is hit by another particle of mass

2 m

moving in the

y

direction with speed

v .

If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:

Important Questions on Work, Energy and Power

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